Recording will always begin at the bar you position the cursor at. If a count-in is enabled it will back up and count you in for 1 or 2 bars before recording begins, just to give you a chance to hear what went before and get ready to come in on time and at speed. But the recording will not begin until the 1 or 2 bar count-in is done and the playhead reaches the bar you positioned it at before you hit record.

You wrote that if the problem project is important to you, you could try creating a new fresh project from scratch. What means from scratch? How it works and what is a scratch?

"From scratch" is an expression that means you start a new, blank (empty) Project. As I'm sure you know, in GarageBand you do this by selecting GB > File menu > New... (shortcut Command-N).

I try to describe, as I can't provide a video right now. I have 3 regions, 2 are small, last one is big. I try to delete first small one, activating it, but the activation (highlight) shows these first 2 smaller ones have become as one middle sized region. If I try to activate the second smaller one, it units with last long one, I mean highlighted are 2 regions together (0nly I clicked on one) and is seen like these 2 ones as one region (the line between the regions has disappeared). So I click on one region to activate it, got activated 2 regions at once and got these 2 ones joined as one. Is it normal? Why it happens?

I understand what you're describing, but I can't duplicate that behavior here. The only ways I can select multiple Regions are by holding Shift and clicking on them, or by drawing a box around them, or by clicking on the Track Header (within a Cycle ruler or when there's no Cycle ruler), and the only way I can combine selected Regions into one Region is with the Join Regions command (Edit menu > Join Regions or Command-J). Maybe you're unintentionally using one of those techniques (i.e. clicking the Track Header or dragging over two Regions or holding Shift without realizing it)..?

https://youtu.be/F2BDpYsTK6c No, I don't use these techniques. I can add a video now, how 2 separate regions become as one. Why it happens? I activate only one, as I want to delete that one. Actually I want to delete them all. Should I activate all three at once?

I don't think you're joining separate Regions at all -- it looks like you're just selecting individual overlapping Regions on that top track (apparently if you move or Trim a Region while holding Command it allows them to overlap). If there are overlapping Regions on the same track then when you select one it just covers up the part of the other Region where the overlap occurs. Try deleting one and I bet it turns out to have been overlapping the adjacent Region -- deleting it should leave the Region below it there in its entirety.

I didn't hold command and I first hear about overlapping region. Anyway, I did as you suggested - I chosed again 1, got 2 again, and then hit delete key on my mac's keyboard. You see, all the 3 regions happily joined to each other... Is that you called "deleting it should leave the region below it there in its entirety" in your last post? As 1 entire region? Sorry, English isn't my tongue. Then why command delete unites the regions, but not disappearing them... ?

the video to my last post. https://youtu.be/Cvc1I5BGndw

Yes, this video shows exactly what I said.. You start with three overlapping Regions -- when you select the short Region in the middle it overlaps the two longer Regions; you delete that short Region, and what's left is the other two longer Regions that had been partially covered up. When you selected the short Region, it covered up sections of the other two Regions -- it overlapped the end of the first longer Region and the beginning of the second longer Region. When you deleted the short overlapping Region, the other two Regions were left there untouched.